Camacho was born in Bayamon, Puerto Rico, to Hector Luis Camacho, Sr., and his wife María Matias. He was the youngest of five children, which included a brother Felix and sisters Raquel, Estrella, and Esperanza. When he was three, his parents separated, and his mother took the children with her to New York City. As an amateur, Camacho won three New York Golden Gloves Championships. Camacho won the 1978 112 lb Sub-Novice Championship, 1979 118 lb Open Championship, and 1980 119 lb Open Championship.